Tracy and Dave together complete the task in [tex]\frac{24}{5}[/tex] hours
Given Tracy alone take 8 hours to complete work and dave alone take 12 hours to complete the work.
Let's say together they worked in x hours
⇒in 1 hour they worked [tex]\frac{1}{x}[/tex]th part of the work
Tracy herself worked 8 hours to complete the whole task
⇒ in 1 hour Tracy completes [tex]\frac{1}{8}[/tex]th part of the task
Dave himself worked 8 hours to complete the whole task
⇒ in 1 hour Dave completes [tex]\frac{1}{12}[/tex]th part of the task
By proportions
⇒[tex]\frac{1}{8}[/tex]+[tex]\frac{1}{12}[/tex]=[tex]\frac{1}{x}[/tex] { using operation addition}
⇒ x= [tex]\frac{24}{5}[/tex]
Therefore,Tracy and Dave together complete the task in [tex]\frac{24}{5}[/tex] hours
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40 scaled to a factor of 0.25
Based on the number being scaled and the scale factor, the value of 40 when scaled to a factor of 0.25 is 10.
How to scale a quantity?When a mathematical problem is given that requires that you scale a certain number by a certain scale factor, you scale that number by multiplying the number by the scale factor.
In this case, the number is 40 and the scale factor is 0.25. When the number is scaled by a factor of 0.25 therefore, we get:
= Number x Scale factor
= 40 x 0.25
= 10
In conclusion, 40 scaled to factor of 0.25 is 10.
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5. What is the domain of the function y = 3x - 4 when the range is (-7, 2, 8, 14}?
A.
{-1, 0, 1, 2}
Y = 3x-4
B.
{-1, 2, 4, 6}
C. {-25, -29, -33, -37}
D. (17, 21, 25, 29}
4413
the domain will be D = { - 1 , 2 , 4 , 6 } for the function y = 3 x - 4.
We are given a function:
y = 3 x - 4
Now we are also given the range as:
R = { -7 , 2 , 8 , 14 }
For y = - 7, we get the value of x as:
- 7 = 3 x - 4
3 x = - 7 + 4
3 x = - 3
x = - 3 / 3
x = - 1
For y = - 2, we get the value of x as:
2 = 3 x - 4
3 x = 2 + 4
3 x = 6
x = 6 / 3
x = 2
For y = 8, we get the value of x as:
8 = 3 x - 4
3 x = 8 + 4
3 x = 12
x = 12 / 3
x = 4
For y = 14, we get the value of x as:
12 = 3 x - 4
3 x = 14 + 4
3 x = 18
x = 18 / 3
x = 6
So, the domain will be:
D = { - 1 , 2 , 4 , 6 }
Therefore, the domain will be D = { - 1 , 2 , 4 , 6 } for the function y = 3 x - 4.
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Rewrite the fraction with a denominator of 30 for 4/5
Answer:
24/30
Step-by-step explanation:
5 goes into 30 6 times, so multiply 4 x 6= 24
Find the other endpoint of the segment with a
midpoint of (-6, 4) and endpoint of (4, 8).
Answer:
(-16, 0)
Step-by-step explanation:
You want the other endpoint of the segment with midpoint (-6, 4) and endpoint (4, 8).
SetupThe midpoint of a line segment has coordinates that are the average of the coordinates of the end points.
M = (A +B)/2 . . . . midpoint M of segment AB
2M = A +B . . . . . multiply by 2
B = 2M -A . . . . . solved for the other end point
B = 2(-6, 4) -(4, 8) . . . . substitute given coordinates
SolutionB = (2(-6) -4, 2(4) -8) = (-16, 0)
The other end point of the segment is (-16, 0).
Find the perimeter and the area of ABCD with vertices A(3, 5), B(6, 5), C(4, -1), and D(1, -1). Round your answer to the nearest hundredth place, if necessary. Perimeter: Area: units square units
The perimeter of the shape is determined as 19.91 units and the area is 20.87 sq. units.
What is perimeter?
The perimeter of an object or a shape is the distance around the edge of the shape.
Length of AB = √[(6 - 3)² + (5 - 5)²] = 3 units
Length of AC = √[(4 - 3)² + (-1 - 5)²] = 6.1 units
Length BD = √[(6 - 1)² + (5 - -1)²] = 7.81 units
Length CD = √[(1 - 4)² + (-1 - -1)²] = 3 units
Perimeter of the shape ABCD = 3 units + 6.1 units + 7.81 units + 3 units = 19.91 units.
Area of the shapeThe formula for area of a trapezoid will be used to determine the area of the shape as shown below;
A = ¹/₂(6.1 + 7.81) x 3
A = 20.87 sq. units
Thus, the perimeter of the shape is determined as 19.91 units and the area is 20.87 sq. units.
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Evaluate 3x+4 for x=3
Answer: 31
Step-by-step explanation:
27 + 4
Calculate the volume of the figure below in cubic feet.
MTH 102 Intermediate Algebra
Two times a number added to another number is 25. Three times the first
number minus the other number is 20. Find the two numbers. (remember to
check your answer).
Let x = the first number and y = the second number
Answer:
mth 102 intermediate algebra 2 times a number added to another number is 25 3 times the first number minus the other number is 25 the two numbers that two numbers of 88 and 72
Answer:
here is my answersssssssssss...enjoy
7th- Grade question
8. A bottle contained 3 7/12 cups of juice. Then Mark drank 1 1/6 cups of the
juice. How much juice was left in the bottle?
A. 2 1/12 cups
B. 2 1/6 cups
C. 2 5/12 cups
D. 2 5/6 cups
Answer:
C
Step-by-step explanation:
3 7/12 - 1 1/6
1. Change 1 1/6 into the same denominator as 3 7/12.
3 7/12 - 1 2/12
2. Subtract whole numbers.
3 - 1 = 2
3. Subtract the fractions.
7/12 - 2/12 = 5/12
4. Answer is 2 5/12 (C).
hope this helps :)
Give the first four terms of the arithmetic sequence
for which a₁ = 12 and d = -2.
A 12, 10, 8, 6
B 12, -24, 48, -96
C 12, 14, 16, 18
D 10, 8, 6, 4
An arithmetic sequence is a sequence of numbers which will have a constant common difference throughout the sequence.
The first term of the sequence is given as a₁ = 12 and
The common difference of the sequence is given as d = -2
We need to find the first four terms of the arithmetic sequence
So, the formula to find the first four terms of an arithmetic sequence is
a, a+d , a+2d, a +3d...
where a = 12
d = -2
Then, the arithmetic sequence of the first four-term is
= 12,12 + (-2) , 12 + 2(-2) , 12 + 3 (-2)
= 12 , 12-2 , 12 -4 , 12 - 6
= 12 , 10 , 8 , 6
So the arithmetic sequence of the first four-term is
12,10,8,6.
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2. At a grocery store, cartons of eggs cost $2.19 each. Identify three points on the graph representing the relationship between the number of cartons purchased and the total cost.
Answer= 0
Step-by-step explanation:
What is 4/6÷4/12?!?!
Answer:2
Step-by-step explanation:
Keep, Change, Flip...4/6 divided by 4/12 = 4/6 * 12/4 which equals 48/24 which when simplified equals 2.
4/6÷4/12 the answer is 2
18. Solve the following equation. (1 point)
96 = -6(-4-3y)
Oy = 2
Oy = 4
Oy = -2
Oy = -4
find the change in temperature from -13c to 15 c math question
Answer:
28 c
Step-by-step explanation:
You want the amount of change from -13c to 15c.
ChangeThe amount of change is found by subtracting the beginning value from the ending value:
(15 c) - (-13 c) = (15 +13) c = 28 c
The temperature changed by 28 c.
2. You transfer into a college with 60 credits. How long will it take you to graduate if you can only take 8
credits per semester? The number of credits needed to graduate is 128. Write an equation for the
number of credits, C, accumulated as a function of the number of semesters, t, at the college.
the function as 17 / 2 = C t for the data given.
Credits we have = 60
credits needed to graduate = 128
Credits in 1 semester = 8
Let the number of semesters be t
Number of credits = C
So, we get the function as:
128 = 60 + 8 C t
128 - 60 = 8 C t
68 = 8 C t
17 / 2 = C t
Therefore, we get that, the function as 17 / 2 = C t for the data given.
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Needing help pretty bad on this one
If anyone can help that’ll be greatly appreciated
Answer:
lol
Step-by-step explanation:
0-2-4-3-5
Find the perimeter of triangle ABC with vertices A(1,-6), B(1,-3), and C(-4,-6). Round to the nearest hundredth if necessary
The perimeter of triangle ABC is equal to 13.83.
PerimeterThe perimeter of a geometric figure is the sum of its sides. Thus, for a triangle, for example, the perimeter is S1+S2+S3, where S represents the dimension of each side.
Given Data
Coordinates Points: A(1,-6), B(1,-3), and C(-4,-6)TriangleIn this question are given the coordinates of each vertex triangle. Then, you should plot these coordinates A(1,-6), B(1,-3), and C(-4,-6) in a graph. See the attached image.
From the plotted points, it is possible to note that the triangle is a right triangle and its sides are: AB=3 and AC=5. For finding the side BC, it is necessary to apply the Pythagorean Theorem: (hypotenuse)²= (side1)²+(side2)². Thus,
(hypotenuse)²= (side1)²+(side2)²
(BC)²=(AB)²+(AC)²
(BC)²=(3)²+(5)²
(BC)²=9+25
(BC)²=34
BC=[tex]\sqrt{34}[/tex]=5.83
Now, you have all information to calculate the perimeter of the given triangle.
perimeter = AB+AC+BC = 3 +5 +5.83 =8+5.83=13.83
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PLEASE HELP ME WITH THIS QUESTION
Please help me to solve this problem!
After plotting the line of the best fit, the estimated values of a and b are
(30,1.15) and the equation is M = 30L ₊ 1.15
Given, the values of L and M are plotted on the graph.
Then the line of best fit is created on the graph.
A line that most accurately depicts the relationship between data points on a scatter plot is called the line of best fit.
When data points appear to be in a straight line, the line of greatest fit is a straight line.
Therefore, we get the point on the line as (30,1.15)
The equation representing the relation:
M = aL + b
(a,b) from the graph is (30,1.15)
substitute the estimated the values,
M = 30L + 1.15
Hence the required values are estimated and plotted on the graph.
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Question
Translate to an equation and solve: Three-tenths of x is 15.
Greetings from Brasil...
know that three-tenths = 0.3
then
0.3X = 15
3X/10 = 15
X = 50questions 32 and 33 please
Answer:
32. AX = BY
33. 3(p - 3q)
Step-by-step explanation:
distribution means multiply through out, the factored value of 3 should should take you back to the original question. 3×p =3p and 3×-3q=-6q
What is the inverse function of this equation
Answer:
y=7x+8
then interchange x and y
x=7y+8
then
x-8=7y
y=X-8/7
What is 1/2a-4 on I ready
If your doing ireadys the answer is 1/2(a-8 but no negative 8 it just original 8
Point Q is between Points A and B on AB, which definition, property, or postulate would justify the equation: AQ + QB = AB
Find the measures of the numbered angles in the figure, shown to the right. Name the theorem that justifies each answer.
Measure
m21-110
m22=110
m23-110
m24 110
Justification
angle whose measure is 70° and Linear Pair Theorem
21 and Alternate Interior Angles Converse
angle whose measure is 70° and Vertical Angles Theorem
21 and Corresponding Angles Converse
GEITS
#
70°
Answer:
interior angle is 70 so go answer my question pls
3. A 6-ounce
package of fruit snacks contains 45
pieces. How many
pieces would you expect in a
10-ounce package?
Answer: 75 pieces
Step-by-step explanation:
The way to answer this question is through simple cross-multiplication.
oz/pieces = 6 oz/45 pieces = 10 oz/x pieces
Cross multiply to get: 6x=450
Simplify: x = 75
Name
Chalisa
Absolute Value
Practice and Problem Solving: C
Average Deviation from Daily Calorie Standard"
Jorge
-125
Rob
+540
Elan
+610
Pietro
-220
Bill
+125
Standard: An active 12-year-old male should consume
about 2,300 calories a day.
Use the table above to answer the questions.
1. Which number acts like a base or 0 in this situation?.
2. Whose calorie consumption is farthest from the standard?
How many calories does he consume?
3. Who consumes the fewest calories?
How many calories does he consume?
4. Which two students' deviations from the standard are opposites?
5. Who consumes a number of calories closest to the standard?
6. Who consumes almost 3,000 calories?
7. What is the average deviation from the standard among these five
students?
8. What is the average absolute deviation from the standard among these
five students?
The above table can be rewritten as
Name Calories Consumed
Jorge 2150
Rob 2840
Elan 2910
Pietro 2080
Bill 2425
Calories Consumed are calculated as standard consumption + deviation
1. the number 2300 acts like a base or 0 in this situation
2. Elan's calorie consumption is farthest from the standard and he consume 2910 calories
3. Pietro consumes the fewest calories and he consume 2080
4. Jorge and Bill's deviations from the standard are opposites
5.Jorge and Bill consumes a number of calories closest to the standard
6.Elan consumes almost 3,000 calories
7.The average deviation from the standard among these five
students is (-125 +540 +610-220 +125)/5 =186 calories
8. the average absolute deviation from the standard among these
five students is 2481 [(2150+2840+ 2910+ 2080+2425)/5]
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The weights of a group of wrestlers is given below. What is the difference between the mean and median weight? {129, 125, 153, 136, 141, 162, 118, 132}
Answer: 957.5
Step-by-step explanation: The mean is 1096, and the median is 138.5
The difference is 957.5
A coach asked her athletes if they enjoy running. Forty-five percent of the team do not like to run. Of those, 70% enjoy cycling, while 80% of those who enjoy running also enjoy cycling. The tree diagram shows how the athletes are divided into subgroups.
a tree diagram shows athletes branching off into two categories of enjoys running and does not enjoy running. Enjoys running branches off into two sub-categories of enjoys cycling and does not enjoy cycling. Does not enjoy running branches off into two sub-categories of enjoys cycling and does not enjoy cycling
What is the total percentage of the athletes who do not enjoy cycling?
50%
24.5%
13.5%
11%
Using proportions, the total percentage of the athletes who do not enjoy cycling is: 24.5%.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For this problem, the proportions of people who do not like cycling are:
0.30 of 0.45(do not like to run).0.2 of 0.55(enjoy running).Hence the total proportion is:
0.3 x 0.45 + 0.2 x 0.55 = 0.245.
Multiplying by 100% to convert from proportion to percentage, 24.5% of the athletes who do not enjoy cycling.
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EASY QUESTION 20 POINTS
Answer:
(c) (-30)⁴
Step-by-step explanation:
You want to simplify the product (-6)⁴×(5)⁴.
ExponentsAn exponent is an indicator of repeated multiplication:
(-6)⁴ = (-6)(-6)(-6)(-6) . . . . . . the factor -6 is repeated 4 times
(5)⁴ = (5)(5)(5)(5)
Then the product is ...
(-6)⁴ × (5)⁴ = (-6)(-6)(-6)(-6)(5)(5)(5)(5)
The commutative and associative properties of multiplication let you regroup this to ...
(-6)(5)×(-6)(5)×(-6)(5)×(-6)(5) = (-30)(-30)(-30)(-30)
Using the exponent to signify repeated multiplication, this can be written as the equivalent ...
(-30)⁴
__
Additional comment
This product has an even number of minus signs, so will be positive. It is fully equivalent to ...
30⁴.